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Re: [Phys-L] uncertainty



On 01/12/2015 12:40 PM, Paul Lulai wrote:
Question 1: If students want to determine the position of a moving
object at a certain time, how do we determine the uncertainty in that
measurement? How reasonable is it for a high school kid to say, "I
measured 40.5cm ± 3cm" based solely on their own confidence in the
measurement? Is there a better way to determine this uncertainty?

Three answers:
a) Absolutely there are better ways.
b) On the other hand, subjective information is better
than no information.
c) More importantly, it may be that the observed value
has no uncertainty whatsoever.

Remember, in all cases, when you talk about uncertainty you
are not talking about numbers per se, but rather a probability
distribution, i.e. a distribution over numbers.

a) If you have a whole bunch of measurements, the observed
distribution tells you pretty much everything you need
to know.
c) If you have only one measurement, it may be that it is
not necessary, desirable, or even possible to talk about
the uncertainty.

I strongly suggest you take a look at
https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian
The observed data points have no size whatsoever. The width
is in the distribution, not in the points. Compare that with
https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian-bars
The "error bars" in the latter figure are completely wrong.

The same idea is expressed again with more points:
https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian-400
which is correct, in contrast to
https://www.av8n.com/physics/probability-intro.htm#fig-frequentist-gaussian-bars-400
which is just completely wrong.

Do not assume that everything needs to have error bars!